Many of the lasting memories from your overseas experience will come from the times you leave your home away from home. Travel within Germany is relatively cheap (with a student travel card) and easy, and getting around Europe is too. Depending on when and how long you choose to study abroad you may have ample opportunity to do some independent exploring. There are many ways to get out of town. Here is a break down of travel both within Germany and abroad.
Travel within Germany
It is possible to get to any point via bus, train, plane, or ferry. While booking your own independent adventure is exciting, also consider traveling with planned tours. Many times there are international student organizations which organize excursions near and far from your home university. Also, in most German students unions, there are travel agents or advisors who will help you get out of town. This makes the logistics of travel easy for you (transportation, accommodation, and some meals are usually included in tours), and it also gives you the opportunity to meet new people and make new friends.